/ (1 + r_ab[p-1] * U(p)*exp(2j*kz[p]*d[p]))
return res
return U(0)
# Power reflexion coefficient for different incidence angles and polarisations
R_th_ss_0 = (abs(ReflectionCoeff(0, 's')))**2 # Phi_i = 0
R_th_ss = (abs(ReflectionCoeff(pi/4, 's')))**2 # Phi_i = pi/4
R_th_pp = (abs(ReflectionCoeff(pi/4, 'p')))**2
############################################################################
# Calculation with Berreman4x4
# Incidence angle Phi_i = 0, 's' polarization
Kx = front.get_Kx_from_Phi(0)
data = numpy.array([s.getJones(Kx, 2*pi/lbda) for lbda in lbda_list])
r_ss = Berreman4x4.extractCoefficient(data, 'r_ss')
R_ss_0 = abs(r_ss)**2
# Incidence angle Phi_i = pi/4, 's' and 'p' polarizations
Kx = front.get_Kx_from_Phi(pi/4)
data = numpy.array([s.getJones(Kx, 2*pi/lbda) for lbda in lbda_list])
r_ss = Berreman4x4.extractCoefficient(data, 'r_ss')
r_pp = Berreman4x4.extractCoefficient(data, 'r_pp')
R_ss = abs(r_ss)**2
R_pp = abs(r_pp)**2
############################################################################
# Plotting
fig = pyplot.figure(figsize=(12., 6.))
pyplot.rcParams['axes.color_cycle'] = ['b','g','r']
ax = fig.add_axes([0.1, 0.1, 0.7, 0.8])
A = -2j*k0*n2*h
R_th = abs((w**2+1)*(1-exp(-2j*k0*n2*h)) \
/ (2*w*(1+exp(-2j*k0*n2*h)) \
- 1j*(w**2-1)*(1-exp(-2j*k0*n2*h))))**2
############################################################################
# Calculation with Berreman4x4
J = numpy.array([s.getJones(Kx,_k0) for _k0 in k0])
# Jones matrices for the circular wave basis
Jc = Berreman4x4.circularJones(J)
power = abs(Jc)**2
# Right-circular wave is reflected in the stop-band
# R_LR, T_LR close to zero
R_RR = Berreman4x4.extractCoefficient(power, 'r_RR')
############################################################################
# Plotting
fig = pyplot.figure()
ax = fig.add_subplot("111")
ax.plot(lbda, R_RR, label='R_RR')
ax.plot(lbda, R_th, 'r', label='R_th')
ax.legend(loc='center right', bbox_to_anchor=(1.00, 0.50))
ax.set_title("Right-handed Cholesteric Liquid Crystal, " +
"{:.1f} helix pitches".format(N/2.))
ax.set_xlabel(r"Wavelength $\lambda_0$ (m)")
ax.set_ylabel(r"Power reflexion $R$")
t2_th_p= (abs((t_bs_p*t_sf_p*exp(1j*kz_s*d)) \
/(1+r_bs_p*r_sf_p*exp(2j*kz_s*d))))**2
correction = real(n_b*cos(Phi_b)/(n_f*cos(Phi_list.astype(complex))))
# This is a correction term used in R +T*correction = 1
T_th_s = t2_th_s*correction
T_th_p = t2_th_p*correction
############################################################################
# Calculation with Berreman4x4
data = numpy.array([s.getJones(kx,k0) for kx in Kx])
data = abs(data)**2
R_p = Berreman4x4.extractCoefficient(data, 'r_pp')
R_s = Berreman4x4.extractCoefficient(data, 'r_ss')
t2_p = Berreman4x4.extractCoefficient(data, 't_pp')
t2_s = Berreman4x4.extractCoefficient(data, 't_ss')
T_s = t2_s*correction
T_p = t2_p*correction
############################################################################
# Plotting
fig = pyplot.figure(figsize=(12., 6.))
pyplot.rcParams['axes.color_cycle'] = ['b','g','r','c','b','g']
ax = fig.add_axes([0.1, 0.1, 0.7, 0.8])
y = numpy.vstack((R_s,R_p,t2_s,t2_p,T_s,T_p)).T
legend1 = ("R_s","R_p","t2_s","t2_p","T_s","T_p")
lines1 = ax.plot(Kx, y)
L = Berreman4x4.RepeatedLayers([L_TiO2, L_SiO2], 8, 0, 1)
# To reduce the number of printed characters in the numbers:
# numpy.set_printoptions(suppress=True, precision=3)
Kx = 0.0
# Structure
s = Berreman4x4.Structure(front, [L], back)
# Calculation
(lbda1, lbda2) = (1.1e-6, 2.5e-6)
lbda_list = numpy.linspace(lbda1, lbda2, 200)
data = numpy.array([s.getJones(Kx, 2*pi/lbda) for lbda in lbda_list])
r = Berreman4x4.extractCoefficient(data, 'r_ss')
R = abs(r)**2
t = Berreman4x4.extractCoefficient(data, 't_ss')
T = s.getPowerTransmissionCorrection(Kx) * abs(t)**2
# Plotting
fig = pyplot.figure()
ax = fig.add_subplot("111")
ax.plot(lbda_list, R, label="$R$")
ax.plot(lbda_list, T, label="$T$")
ax.legend(loc='center right')
ax.set_xlabel(r"Wavelength $\lambda$ (m)")
ax.set_ylabel(r"Power reflection $R$ or transmission $T$")
ax.set_title(r"Bragg mirror: Air/{TiO$_2$/SiO$_2$}x8/TiO$_2$/Glass")
def plotTransmission(label):
"""Plots power transmission vs. wavenumber."""
data = numpy.array([s.getJones(Kx,k0) for k0 in k0_list])
t_pp = Berreman4x4.extractCoefficient(data, 't_pp')
T = abs(t_pp)**2 # valid if back and front media are identical
ax.plot(k0_list, T, 'x', label=label)
# Calculation parameters lbda_min, lbda_max = 0.8e-6, 1.2e-6 # (m) lbda_B = p * n_med lbda_list = numpy.linspace(lbda_min, lbda_max, 100) k0_list = 2*pi/lbda_list ############################################################################ # Analytical calculation for the maximal reflection R_th = numpy.tanh(Dn/n_med*pi*h/p)**2 lbda_B1, lbda_B2 = p*no, p*ne ############################################################################ # Calculation with Berreman4x4 J = numpy.array([s.getJones(Kx,k0) for k0 in k0_list]) power = abs(J)**2 T_pp = Berreman4x4.extractCoefficient(power, 't_pp') T_ps = Berreman4x4.extractCoefficient(power, 't_ps') T_ss = Berreman4x4.extractCoefficient(power, 't_ss') T_sp = Berreman4x4.extractCoefficient(power, 't_sp') # Note: the expression for T is valid if back and front media are identical # Transmission coefficients for incident unpolarized light: T_pn = 0.5 * (T_pp + T_ps) T_sn = 0.5 * (T_sp + T_ss) T_nn = T_sn + T_pn # Transmission coefficients for 's' and 'p' polarized light, with # unpolarized measurement. T_ns = T_ps + T_ss T_np = T_pp + T_sp
IL = Berreman4x4.InhomogeneousLayer(TN)
# IL.setMethod("symplectic","Padé",3)
# Structure
s = Berreman4x4.Structure(front, [IL], back)
# Normal incidence:
Kx = 0.0
# Calculation
lbda_min, lbda_max = 200e-9, 1 # (m)
k0_list = numpy.linspace(2*pi/lbda_max, 2*pi/lbda_min)
data = [s.getJones(Kx,k0) for k0 in k0_list]
data = numpy.array(data)
t_pp = Berreman4x4.extractCoefficient(data, 't_pp')
# Plotting
fig = pyplot.figure()
ax = fig.add_subplot("111")
ax.plot(k0_list, abs(t_pp)**2, 'o', label="Berreman4x4")
# Verification with Gooch-Tarry law:
u = 2*d*Dn*k0_list/(2*pi)
T_GT = sin(pi/2*sqrt(1+u**2))**2 / (1+u**2)
ax.plot(k0_list, T_GT, label="Gooch-Tarry")
ax.set_title(u"Transmission of a 90° twisted nematic liquid crystal")
ax.set_xlabel(r"Wavenumber $k_0$ (m$^{-1}$)")
ax.set_ylabel(r"Power transmission, $T$")
ax.legend()
